{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,14]],"date-time":"2026-03-14T22:05:35Z","timestamp":1773525935941,"version":"3.50.1"},"reference-count":46,"publisher":"MDPI AG","issue":"3","license":[{"start":{"date-parts":[[2023,3,1]],"date-time":"2023-03-01T00:00:00Z","timestamp":1677628800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>One of the most used techniques for determining animal abundance is distance sampling. The distance sampling framework depends on the idea of a detection function, and a number of options have been suggested. In this paper, we provide a new flexible parametric model based on the Burr XII distribution. To be more specific, we use the survival function of the Burr XII distribution for novel purposes in this context. The proposed model is appealing because it meets all of the requirements for a reliable detection function model, such as being monotonically decreasing and having a shoulder at the origin. It also has the features of having various asymmetric properties and a heavy right tail, which are rare properties in this setting. In the first part, we provide its key characteristics, such as shapes and moments. Then, the inferential aspect of the model is investigated. The maximum likelihood estimation method is used to estimate the parameters in a data-fitting scenario. The estimates of population abundance are derived and compared with some existing parametric estimates. A simulation is run to assess how well the resulting estimates perform in comparison to other widely applied estimates from the literature. The model is then tested using two real-world data sets. Based on the famous goodness-of-fit statistics, we show that it is preferable to some of the well-established models.<\/jats:p>","DOI":"10.3390\/sym15030620","type":"journal-article","created":{"date-parts":[[2023,3,1]],"date-time":"2023-03-01T03:03:48Z","timestamp":1677639828000},"page":"620","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":3,"title":["A New Detection Function Model for Distance Sampling Based on the Burr XII Model"],"prefix":"10.3390","volume":"15","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-5337-2276","authenticated-orcid":false,"given":"Ayed R. A.","family":"Alanzi","sequence":"first","affiliation":[{"name":"Department of Mathematics, College of Science and Arts in Gurayat, Jouf University, Gurayat 77454, Saudi Arabia"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-6192-9890","authenticated-orcid":false,"given":"Farrukh","family":"Jamal","sequence":"additional","affiliation":[{"name":"Department of Statistics, Faculty of Computing, The Islamia University, Bahawalpur 63100, Pakistan"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-2157-3997","authenticated-orcid":false,"given":"Muhammad H.","family":"Tahir","sequence":"additional","affiliation":[{"name":"Department of Statistics, Faculty of Computing, The Islamia University, Bahawalpur 63100, Pakistan"}]},{"given":"Christophe","family":"Chesneau","sequence":"additional","affiliation":[{"name":"Department of Mathematics, LMNO, University of Caen, 14032 Caen, France"}]},{"given":"Sana","family":"Kanwal","sequence":"additional","affiliation":[{"name":"Department of Statistics, Faculty of Computing, The Islamia University, Bahawalpur 63100, Pakistan"}]},{"given":"Waqas","family":"Sami","sequence":"additional","affiliation":[{"name":"College of Nursing, QU Health, Qatar University, Doha P.O. Box 2713, Qatar"}]}],"member":"1968","published-online":{"date-parts":[[2023,3,1]]},"reference":[{"key":"ref_1","first-page":"3","article-title":"Estimation of density from line transect sampling of biological populations","volume":"72","author":"Burnham","year":"1980","journal-title":"Wildl. Monogr."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"135","DOI":"10.2307\/2528465","article-title":"Line transect method of estimating grouse population densities","volume":"24","author":"Gates","year":"1968","journal-title":"Biometrics"},{"key":"ref_3","unstructured":"Hemingway, P. (1971). The Scientific Management of Animal and Plant Communities for Conservation, Blackwell."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"325","DOI":"10.2307\/2529501","article-title":"Mathematical models for nonparametric inferences from line transect data","volume":"32","author":"Burnham","year":"1976","journal-title":"Biometrics"},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"475","DOI":"10.2307\/2530611","article-title":"A family of density estimators for line-transect sampling","volume":"34","author":"Pollock","year":"1978","journal-title":"Biometrics"},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"505","DOI":"10.1093\/biomet\/66.3.505","article-title":"Parametric models for line transect surveys","volume":"66","author":"Ramsey","year":"1979","journal-title":"Biometrika"},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"1325","DOI":"10.2307\/2533263","article-title":"Bayesian estimation of animal abundance for line transect sampling","volume":"51","author":"Karunamuni","year":"1995","journal-title":"Biometrics"},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"177","DOI":"10.2307\/2530653","article-title":"Perpendicular distance models for line transect sampling","volume":"41","author":"Buckland","year":"1985","journal-title":"Biometrics"},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"1","DOI":"10.2307\/3800685","article-title":"Transect methods for population studies","volume":"42","author":"Eberhardt","year":"1978","journal-title":"J. Wildl. Manag."},{"key":"ref_10","first-page":"315","article-title":"A parametric family for density estimation in line transect sampling","volume":"13","author":"Eidous","year":"2004","journal-title":"Basic Sci. Eng."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"11","DOI":"10.22237\/jmasm\/1335845400","article-title":"A weighted exponential detection function model for line transect data","volume":"11","author":"Ababneh","year":"2012","journal-title":"J. Mod. Appl. Stat. Methods"},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"293","DOI":"10.2307\/1935188","article-title":"Parametric Models for Line-Transect Estimators of Abundance","volume":"61","author":"Quinn","year":"1980","journal-title":"Ecology"},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"3675","DOI":"10.1080\/03610926.2017.1361987","article-title":"A bias-corrected histogram estimator for line transect sampling","volume":"47","author":"Eidous","year":"2018","journal-title":"Commun.-Stat.-Theory Methods"},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"901","DOI":"10.2307\/2532356","article-title":"A robust line transect method","volume":"48","author":"Buckland","year":"1992","journal-title":"Biometrics"},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"2147","DOI":"10.1139\/z01-174","article-title":"Comparing movement patterns of satellite-tagged male and female polar bears","volume":"79","author":"Amstrup","year":"2001","journal-title":"Can. J. Zool."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"311","DOI":"10.1007\/BF00539369","article-title":"A combination line transect and capture-recapture sampling model for multiple observers in aerial surveys","volume":"3","author":"Pollock","year":"1996","journal-title":"Environ. Ecol. Stat."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"207","DOI":"10.1198\/jabes.2009.0013","article-title":"A gamma-shaped detection function for line-transect surveys with mark-recapture and covariate data","volume":"14","author":"Becker","year":"2009","journal-title":"J. Agric. Biol. Environ. Stat."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"663","DOI":"10.1080\/01621459.1952.10483446","article-title":"A generalization of sampling without replacement from a finite universe","volume":"47","author":"Horvitz","year":"1952","journal-title":"J. Am. Stat. Assoc."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"1221","DOI":"10.2307\/2533652","article-title":"Horvitz-Thompson estimators for double-platform line transect surveys","volume":"54","author":"Borchers","year":"1998","journal-title":"Biometrics"},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"349","DOI":"10.1046\/j.1365-2664.2001.00584.x","article-title":"Estimating deer abundance from line transect surveys of dung: Sika deer in southern Scotland","volume":"38","author":"Marques","year":"2001","journal-title":"J. Appl. Ecol."},{"key":"ref_21","first-page":"413","article-title":"Local likelihood density estimation in line transect sampling","volume":"11","author":"Barabesi","year":"2000","journal-title":"Environ. Off. J. Int. Environ. Soc."},{"key":"ref_22","first-page":"301","article-title":"Nonparametric Estimation of f(0) Applying Line Transect Data with and without the Shoulder Condition","volume":"36","author":"Eidous","year":"2015","journal-title":"J. Inf. Optim. Sci."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"15","DOI":"10.13189\/ms.2016.040102","article-title":"One-term approximation for normal distribution function","volume":"4","author":"Eidous","year":"2016","journal-title":"Math. Stat."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"893","DOI":"10.1214\/09-AOAS307","article-title":"Density estimation for grouped data with application to line transect sampling","volume":"4","author":"Jang","year":"2010","journal-title":"Ann. Appl. Stat."},{"key":"ref_25","unstructured":"Seber, G.A.F. (1982). The Estimation of Animal Abundance and Related Parameters, Macmillan Publishing Company."},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"443","DOI":"10.1198\/108571104X15601","article-title":"Zigzag survey designs in line transect sampling","volume":"9","author":"Strindberg","year":"2004","journal-title":"J. Agric. Biol. Environ. Stat."},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"230","DOI":"10.2307\/1400405","article-title":"Combining line transect and double count sampling techniques for aerial surveys","volume":"2","author":"Quang","year":"1997","journal-title":"J. Agricult. Biol. Environ. Stat."},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"13","DOI":"10.2307\/2531944","article-title":"Size bias in line transect sampling","volume":"43","author":"Drummer","year":"1987","journal-title":"Biometrics"},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"1248","DOI":"10.2307\/3801785","article-title":"The need for distance data in transect counts","volume":"48","author":"Burnham","year":"1984","journal-title":"J. Wildl. Manag."},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"402","DOI":"10.2307\/3808843","article-title":"Confidence limits for line transect estimates based on shape restrictions","volume":"57","author":"Routledge","year":"1992","journal-title":"J. Wildl. Manag."},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"348","DOI":"10.2307\/3809401","article-title":"Evaluation of walked line transect counts for estimating macropod density","volume":"58","author":"Southwell","year":"1994","journal-title":"J. Wildl. Manag."},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"519","DOI":"10.1016\/j.dsr.2008.01.005","article-title":"Uncommon or cryptic? Challenges in estimating leopard seal abundance by conventional but state-of-the-art methods","volume":"55","author":"Southwell","year":"2008","journal-title":"Deep. Sea Res. Part I Oceanogr. Res. Pap."},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"93","DOI":"10.1002\/ajp.1350290203","article-title":"Estimation of density of gibbon groups by use of loud songs","volume":"29","author":"Brockelman","year":"1993","journal-title":"Am. J. Primatol."},{"key":"ref_34","first-page":"135","article-title":"A kernel estimate for the density of a biological population by using line transect sampling","volume":"45","author":"Chen","year":"1996","journal-title":"J. R. Stat. Soc. Ser. Appl. Stat."},{"key":"ref_35","doi-asserted-by":"crossref","first-page":"1130","DOI":"10.1111\/j.0006-341X.2001.01130.x","article-title":"Line transect sampling in small regions","volume":"57","author":"Melville","year":"2001","journal-title":"Biometrics"},{"key":"ref_36","doi-asserted-by":"crossref","first-page":"229","DOI":"10.2307\/2667087","article-title":"Cultural diversity at work: The effects of diversity perspectives on work group processes and outcomes","volume":"46","author":"Ely","year":"2001","journal-title":"Adm. Sci. Q."},{"key":"ref_37","doi-asserted-by":"crossref","first-page":"221","DOI":"10.1071\/WR10234","article-title":"The importance of survey design in distance sampling: Field evaluation using domestic sheep","volume":"38","author":"Porteus","year":"2011","journal-title":"Wildl. Res."},{"key":"ref_38","doi-asserted-by":"crossref","first-page":"299","DOI":"10.1071\/WR07034","article-title":"Visibility bias in aerial survey: Mark\u2013recapture, line-transect or both?","volume":"35","author":"Laake","year":"2008","journal-title":"Wildl. Res."},{"key":"ref_39","doi-asserted-by":"crossref","first-page":"317","DOI":"10.1002\/jwmg.216","article-title":"Using distance sampling and hierarchical models to improve estimates of Dall\u2019s sheep abundance","volume":"76","author":"Schmidt","year":"2012","journal-title":"J. Wildl. Manag."},{"key":"ref_40","doi-asserted-by":"crossref","first-page":"275","DOI":"10.1071\/WR07077","article-title":"The influence of animal mobility on the assumption of uniform distances in aerial line-transect surveys","volume":"35","author":"Fewster","year":"2008","journal-title":"Wildl. Res."},{"key":"ref_41","doi-asserted-by":"crossref","first-page":"129","DOI":"10.1093\/biomet\/64.1.129","article-title":"A guide to the Burr type XII distributions","volume":"64","author":"Rodriguez","year":"1977","journal-title":"Biometrika"},{"key":"ref_42","doi-asserted-by":"crossref","first-page":"59","DOI":"10.1016\/0893-9659(91)90123-D","article-title":"A characterization of the Burr type XII distribution","volume":"4","year":"1991","journal-title":"Appl. Math. Lett."},{"key":"ref_43","doi-asserted-by":"crossref","first-page":"20","DOI":"10.1016\/j.csda.2013.02.026","article-title":"Power Lindley distribution and associated inference","volume":"64","author":"Ghitany","year":"2013","journal-title":"Computational Stat. Data Anal."},{"key":"ref_44","unstructured":"Wackerly, D., Mendenhall, W., and Scheaffer, R.L. (2014). Mathematical Statistics with Applications, Cengage Learning."},{"key":"ref_45","unstructured":"Saeed, G.A.A. (2013). New Parametric Model for Grouped and Ungrouped Line Transect Data. [Ph.D. Thesis, Yarmouk University]."},{"key":"ref_46","doi-asserted-by":"crossref","first-page":"2343","DOI":"10.1081\/STA-100107690","article-title":"Generalized likelihood ratio test for the shoulder condition in line transect sampling","volume":"30","author":"Zhang","year":"2001","journal-title":"Commun. Stat.-Theory Methods"}],"container-title":["Symmetry"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2073-8994\/15\/3\/620\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T18:44:59Z","timestamp":1760121899000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2073-8994\/15\/3\/620"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2023,3,1]]},"references-count":46,"journal-issue":{"issue":"3","published-online":{"date-parts":[[2023,3]]}},"alternative-id":["sym15030620"],"URL":"https:\/\/doi.org\/10.3390\/sym15030620","relation":{},"ISSN":["2073-8994"],"issn-type":[{"value":"2073-8994","type":"electronic"}],"subject":[],"published":{"date-parts":[[2023,3,1]]}}}